The thermodynamic functions of fullerene derivative (t-Bu)12C60 over the temperature range from T → 0 to 420 K

Heat Capacity and Standard Thermodynamic Functions of a Fullerene Complex, ((CH3)3Si)12C60, over the Range fromT→ 0 K toT= 350 K

“…In the fractal version of Debye’s theory of the heat capacity of solids, − the exponent of T in the expression for heat capacity is referred to as fractal dimension. The values of this key parameter denoted by D were determined from experimental results on the heat capacity of ((CH 3 ) 3 Si) 12 C 60 and literature data for C 60 fullerite and ( t -Bu) 12 C 60 (Table ). The values of D were estimated using the technique described, for example, in ref with the use of eq C v = 3 D ( D + 1 ) k N γ ( D + 1 ) ξ ( D + 1 ) ( T / Θ max ) where N is the number of atoms in a molecule, k is the Boltzmann constant, γ( D + 1) is the γ-function, ξ( D + 1) is the Riemann ξ-function, and Θ max is the characteristic temperature.…”

“…In Figure , the temperature dependence of the molar heat capacity C p ,m o for ((CH 3 ) 3 Si) 12 C 60 (curve 1), ( t -Bu) 12 C 60 (curve 2), and fullerite C 60 (curve 3) are shown. As can be learned, the molar heat capacities of ((CH 3 ) 3 Si) 12 C 60 and ( t -Bu) 12 C 60 are higher than the heat capacity of C 60 .…”

“…Curves of smoothed molar heat capacities of ((CH 3 ) 3 Si) 12 C 60 (1), ( t -Bu) 12 C 60 (2), and C 60 (3).…”

“…The experimental points of C p,m o in the temperature range between T ) (6 and 350) K were fitted by means of the leastsquares method, and the polynomial equations of the C p,m o versus temperature is the following: for the range from T ) (7 to 22) K, ) A + B ln(T/30) + C(ln(T/30)) 2 + D(ln(T/30)) 3 + E(ln(T/30)) 4 + F(ln(T/30)) 5 + G(ln(T/30)) 6 + H(ln(T/30)) 7 + I(ln(T/30)) 8 (1)…”

“…The purpose of the present study is to measure the low-temperature heat capacities by adiabatic calorimetry over the temperature range T = (6.5 to 350) K of the crystalline fullerene complex ((CH 3 ) 3 Si) 12 C 60 , to calculate the standard thermodynamic functions: C p ,m o , H o ( T ) − H o (0), S o ( T ), and G o ( T ) − H o (0) of ((CH 3 ) 3 Si) 12 C 60 (cr) over the range from T → 0 K to T = 350 K, to determine the characteristic temperatures and fractal dimension D , to establish the structure topology, to calculate the standard entropy of formation at T = 298.15 K of ((CH 3 ) 3 Si) 12 C 60 (cr), and to compare the thermodynamic characteristics of the fullerene complex under study, C 60 and ( t -Bu) 12 C 60 …”